How to make my C++ library compliant with IEEE 754

I have written a small library (in C++11) to compute with quaternions, but I quickly realized there are many precision/accuracy issues given that quite a few floating point operations are involved. That lead me to looking at std::complex and IEEE 754. std::complex does a fair amount of work dealing with NaNs in particular. Is that the only thing I need to worry about to become "IEEE 754 compliant"? More generally, is there a "recipe" for how to turn an otherwise naive numerical library into one that would be "IEEE 754 compliant"?